Algebra part 3

c.Pemangkatan Suku Tunggal

Perhatikan perkalian bentuk aljabar berikut.

b^2 = b x b
(-b)^2 = (-b) x (-b)
-(b)^2 = - (b x b)
(2b)^2 = 2b x 2b = 4b^2

Tentukan hasil pemangkatan bentuk aljabar berikut ini.

1. (4k)^2
2. (-2y)^2
3. -(5q)^3
4. (-3t^2)^3
5. (2a x 3 b)^4
6. (2p^2q x pq^2)^2

Penyelesaian:
1.(4k)^2 = 4k x 4k = 4 x 4 x k x k=16k^2
2. (-2y)^2 = (-2y) x (-2y) = (-2) x (-2) x y x y =4y^2
3.-(5q)^3 =- (5q x 5q x5q)=-(5 x 5 x 5 x q x q x q)=-(125q^3)=-125p^3
4.(-3t^2)^3 = -3t^2 x (-3t^2) x (-3t^2)
= -3 x -3 x-3 x t^2 x t^2 x t^2
=-27t^6
5.(2a x 3b)^4= (2a x 3b)x (2a x 3b) x (2a x 3b) x (2a x 3b)
= 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x a x a x a x a x b x b x b x b
= 16 x 81 x a^4 x b^4
= 1296 a^4b^4
6.(2p^2 q x pq^2)^2 = (2p^2 q x pq^2) x (2p^2 q x pq^2)
= 2 x 2 x p^2 x p^2 x p x p x q x q x q^2 x q^2)
= 4 x p^6 x q^6
= 4p^6q^6